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Laurent Corté

à 11h en salle C. Brot

Many-body systems often exhibit irreversible behavior even though the governing
equations of motion are reversible. Nevertheless, it is unusual to encounter a physical
system in which the transition from reversible to irreversible behavior can be explored
experimentally.
Recent experiments on periodically sheared non-Brownian suspensions showed a
sharp transition from reversible to irreversible chaotic behavior above a concentration
dependent threshold strain amplitude gC [1]. For a given particle volume fraction, two
regimes are obtained depending on the shear strain amplitude. Below gC, most of the
particles have reversible trajectories and return to their initial positions at the end of
each shear cycle. Above gC, reversibility is lost and particles are displaced irreversibly
due to shear-induced diffusion. The irreversibility of particle trajectories in
suspensions is well-known. It is related to shear-induced diffusion and to chaos. The
observation of such a sharp threshold however is puzzling as the initial distribution of
particles is random, with no obvious mechanism for the onset of irreversibility.
We develop a simple model, explored through simulation and mean field theory, which
captures the salient behavior of the experiments. For small strain amplitude, the
model reveals that random displacements of colliding particles can cause the system
to self-organize into a reversible state that avoid further collisions. This model and
additional experiments show that the strain threshold actually corresponds to the
critical point of a non-equilibrium phase transition between absorbing and active
fluctuating states [2]. These results provide new insights into how microstructure can
spontaneously develop and how random encounters can help a system evolve towards
a stable fixed point. In particular, we will see how non-colloidal suspensions under
slow periodic shear could constitute new model systems for the study of critical
phenomena in dynamical systems.
[1] Pine D.J., Gollug J.P., Brady J.F., Leshansky A.M. Nature 438, 997-1000, (2005).
[2] Corté L., Chaikin P.M., Gollub J.P., Pine D.J. Nature Physics 4, 420-424, (2008).